snowbirdskier wrote:
Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000
The table above shows the total sales recoreded in July for the 5 salespeople at Acme Truck Sales. It was discovered that one of Cal's sales was incorrectly recorded as one of Ann's sales. After this error was corrected, Ann's total sales were still higher than Cal's total sales, and the median of the 5 sales totals was $330,000. What was the value of the incorrectly recorded sale? (GMAT practice test)
There are 5 values given to us and their median is 330 (Let's ignore the extra 0s). What does that mean?
Say there is a list of numbers: 4, 6, 9, 12, 35
How do you get the median? It is the middle value in case you have odd number of values in increasing/decreasing order. It doesn't matter what the other values are. Median is equal to the value right in the middle.
If median of a list of 5 values is 330, it means that 330 must be one of the 5 values. 2 values must be greater than 330 and 2 must be smaller than 330.
Let me arrange the given list in decreasing order:
Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000
680,
450, 360, 210,
190I cannot touch the other 3 values (Just the red ones (Ann's and Cal's)). Since 680 and 360 remain and are greater than 330, so my actual list should look something like this:
680, 360, 330, ....., ..... (210 occupies one of these blanks)
The question now is: To whom does this 330 belong?
If Ann's sales decreases from 450 to 330, Cal's sale should increase by 120 (= 450 - 330) i.e. Cal's actual sales should be 190 + 120 = 310.
The list becomes: 680, 360, 330, 310, 210 - satisfies everything. The value of the incorrectly recorded sales must have been $120,000.
Could 330 belong to Cal? Then Cal's sales would have increased by 330 - 190 = 140
Ann's sales would have decreased by 140 to get her actual sales of 310. But it is given that Ann's sales remains higher than Cal's. Hence this is not possible.
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Karishma
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